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Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors

Year 2022, Volume: 10 Issue: 2, 240 - 249, 31.10.2022

Tuğba Mert Mehmet Atçeken Pakize Uygun

Abstract

In this article, semi-symmetric generalized Sasakian space forms are investigated on some special curvature tensors. Characterizations of generalized Sasakian space forms are obtained on some specially selected $\sigma-$curvature tensors. By examining the flatness of these $\sigma -$curvature tensors, the properties of generalized sasakian space forms are given. More importantly, the cases of $\sigma-$semi-symmetric generalized Sasakian space forms are discussed and the behavior of the manifold is examined for each case. Again, necessary and sufficient conditions have been obtained for $\sigma-$symmetric generalized Sasakian space forms to be Einstein manifolds.

Keywords

σ-Curvature Tensors Semi-Symmetric Manifold Sasakian Space Forms

References

  • [­1] Alegre P., Blair D.E and Carriazo A., Generalized Sasakian space form. Israel journal of Mathematics, 141 (2004), 157-183.
  • [2] De U.C. and Sarkar A., On the projective curvature tensor of generalized Sasakian space forms, Quaestines Mathematicae, 33 (2010), 245-252.
  • [3] Sarkar A. and De U.C., Some curvature properties of generalized Sasakian space forms, Lobachevskii journal of mathematics, 33 (2012), no.1, 22-27.
  • [4] O¨ zgu¨r C. and Tripathi N.M., On P-Sasakian manifolds satisfying certain conditions on concircular curvature tensor, Turk. J. Math., 31 (2007), 171-179.
  • [5] Atc¸eken M., On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Math. Analysis and Applications, vol.6, 1 (2014), 1-8.
  • [6] Sreenivasa G.T., Venkatesha and Bagewadi C.S., Some Results on (LCS)2n+1􀀀Manifolds, Bulletin of mathematical analysis and applications, vol.1, 3 (2009).
  • [7] Alegre P. and Cariazo A., Structures on generalized Sasakian-space-form, Differential Geom. and its application 26 (2008), 656–666.
  • [8] Belkhelfa M., Deszcz R. and Verstraelen L., Symmetry properties of Sasakianspace-forms, Soochow Journal of Mathematics 31 (2005), 611–616.
  • [9] Kim U.K., Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note di matemetica 26 (2006), 55–67.
  • [10] M. Tripathi, P. Gupta, t􀀀Curvature Tensor on A Semi-Riemannian Manifold, J. Adv. Math. Studies, 4 (2011), 117-129.
  • [11] M. Atc¸eken and P. Uygun, Characterizations for totally geodesic submanifolds of (k;m)􀀀paracontact metric manifolds, Korean J. Math. 28(2020), 555-571.
  • [12] T. Mert, Characterization of some special curvature tensor on Almost C(a)􀀀manifold, Asian Journal of Math. and Computer Research, 29 (1)(2022), 27-41.
  • [13] T. Mert and M. Atc¸eken, Almost C(a)􀀀manifold onW 0 -curvature tensor, Applied Mathematical Sciences, 15 (15) (2021), 693-703.
  • [14] M. Atc¸eken, Some results on invariant submanifolds of Lorentzian para-Kenmotsu manifolds, Korean J. Math., 30 (1) (2022), 175-185.
  • [15] M. Atc¸eken, T. Mert, Characterizations for totally geodesic submanifolds of a K􀀀paracontact manifold, AIMS Math., 6 (7) (2021), 7320-7332.
  • [16] T. Mert, M. Atc¸eken, Almost C(a)􀀀manifoldon M􀀀projectively curvature tensor, New Trends in Mathematical Sciences, 10 (3) (2022), 1-8.
  • [17] P. Uygun, S.Dirik, M, Atc¸eken and T.Mert, Some Characterizations Invariant Submanifolds of A (k;m)􀀀Para Contact Space, Journal of Engineering Research and Applied Science, 11 (1) (2022), 1967-1972.

Year 2022, Volume: 10 Issue: 2, 240 - 249, 31.10.2022

Tuğba Mert Mehmet Atçeken Pakize Uygun

Abstract

References

  • [­1] Alegre P., Blair D.E and Carriazo A., Generalized Sasakian space form. Israel journal of Mathematics, 141 (2004), 157-183.
  • [2] De U.C. and Sarkar A., On the projective curvature tensor of generalized Sasakian space forms, Quaestines Mathematicae, 33 (2010), 245-252.
  • [3] Sarkar A. and De U.C., Some curvature properties of generalized Sasakian space forms, Lobachevskii journal of mathematics, 33 (2012), no.1, 22-27.
  • [4] O¨ zgu¨r C. and Tripathi N.M., On P-Sasakian manifolds satisfying certain conditions on concircular curvature tensor, Turk. J. Math., 31 (2007), 171-179.
  • [5] Atc¸eken M., On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Math. Analysis and Applications, vol.6, 1 (2014), 1-8.
  • [6] Sreenivasa G.T., Venkatesha and Bagewadi C.S., Some Results on (LCS)2n+1􀀀Manifolds, Bulletin of mathematical analysis and applications, vol.1, 3 (2009).
  • [7] Alegre P. and Cariazo A., Structures on generalized Sasakian-space-form, Differential Geom. and its application 26 (2008), 656–666.
  • [8] Belkhelfa M., Deszcz R. and Verstraelen L., Symmetry properties of Sasakianspace-forms, Soochow Journal of Mathematics 31 (2005), 611–616.
  • [9] Kim U.K., Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note di matemetica 26 (2006), 55–67.
  • [10] M. Tripathi, P. Gupta, t􀀀Curvature Tensor on A Semi-Riemannian Manifold, J. Adv. Math. Studies, 4 (2011), 117-129.
  • [11] M. Atc¸eken and P. Uygun, Characterizations for totally geodesic submanifolds of (k;m)􀀀paracontact metric manifolds, Korean J. Math. 28(2020), 555-571.
  • [12] T. Mert, Characterization of some special curvature tensor on Almost C(a)􀀀manifold, Asian Journal of Math. and Computer Research, 29 (1)(2022), 27-41.
  • [13] T. Mert and M. Atc¸eken, Almost C(a)􀀀manifold onW 0 -curvature tensor, Applied Mathematical Sciences, 15 (15) (2021), 693-703.
  • [14] M. Atc¸eken, Some results on invariant submanifolds of Lorentzian para-Kenmotsu manifolds, Korean J. Math., 30 (1) (2022), 175-185.
  • [15] M. Atc¸eken, T. Mert, Characterizations for totally geodesic submanifolds of a K􀀀paracontact manifold, AIMS Math., 6 (7) (2021), 7320-7332.
  • [16] T. Mert, M. Atc¸eken, Almost C(a)􀀀manifoldon M􀀀projectively curvature tensor, New Trends in Mathematical Sciences, 10 (3) (2022), 1-8.
  • [17] P. Uygun, S.Dirik, M, Atc¸eken and T.Mert, Some Characterizations Invariant Submanifolds of A (k;m)􀀀Para Contact Space, Journal of Engineering Research and Applied Science, 11 (1) (2022), 1967-1972.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Tuğba Mert

Mehmet Atçeken 0000-0002-1242-4359

Pakize Uygun

Publication Date October 31, 2022
Submission Date June 22, 2022
Acceptance Date August 31, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Mert, T., Atçeken, M., & Uygun, P. (2022). Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors. Konuralp Journal of Mathematics, 10(2), 240-249.
AMA Mert T, Atçeken M, Uygun P. Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors. Konuralp J. Math. October 2022;10(2):240-249.
Chicago Mert, Tuğba, Mehmet Atçeken, and Pakize Uygun. “Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 240-49.
EndNote Mert T, Atçeken M, Uygun P (October 1, 2022) Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors. Konuralp Journal of Mathematics 10 2 240–249.
IEEE T. Mert, M. Atçeken, and P. Uygun, “Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors”, Konuralp J. Math., vol. 10, no. 2, pp. 240–249, 2022.
ISNAD Mert, Tuğba et al. “Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors”. Konuralp Journal of Mathematics 10/2 (October 2022), 240-249.
JAMA Mert T, Atçeken M, Uygun P. Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors. Konuralp J. Math. 2022;10:240–249.
MLA Mert, Tuğba et al. “Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors”. Konuralp Journal of Mathematics, vol. 10, no. 2, 2022, pp. 240-9.
Vancouver Mert T, Atçeken M, Uygun P. Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors. Konuralp J. Math. 2022;10(2):240-9.
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